Active flow control of laminar boundary layers for variable flow conditions

https://doi.org/10.1016/j.ijheatfluidflow.2015.09.003Get rights and content

Highlights

  • We do active wave cancelation of broad-band Tollmien–Schlichting waves.

  • The transmission behavior of the boundary layer changes with flow speed.

  • The fxLMS controller can adapt to slight changes of the flow speed.

  • A phase error of ± 90 deg. can be adapted by the fxLMS algorithm.

  • The stable operation range can be extended by an adaptive secondary path model.

Abstract

This work investigates the stability of a fxLMS controller for active wave cancelation of broad-band Tollmien–Schlichting disturbances in a flat plate boundary-layer with a single DBD plasma actuator. In particular the influence of a changing free stream velocity and the resulting off-design operation of the control algorithm is analyzed up to an unstable behavior. As the main reason for unstable controller operation in the off-design case the difference between actual and predicted phase angle of the disturbances at the position of the error sensor is identified. A method for an online adjustment of the secondary-path model to different free-stream velocities is presented. Finally a wall-bounded method based on the disturbances phase speed is developed that can cope with changes of the physical secondary path not only due to changes of the free-stream velocity but also due to changes of the pressure distribution. This method enables the extension of the stable operation range of the control system significantly.

Introduction

The laminar-turbulent transition in boundary-layer flows has been extensively investigated in the last decades and most mechanisms are well understood (Saric, Reed, Kerschen, 2002, Würz, Sartorius, Kloker, Borodulin, Kachanov, Smorodsky, 2012). Modern composite materials and accompanying smooth surfaces allow the successful application of NLF (natural laminar flow) airfoils, especially for gliders, ultra-light airplanes and UAVs. The special design of the NLF airfoils causes an acceleration of the boundary-layer flow for a high percentage of chord and therefore a favorable pressure gradient with laminar flow (Joslin, 1998). The goal is a reduction of skin-friction drag by keeping the boundary layer laminar and avoiding the transition to turbulence. Besides the airfoil shape and surface quality active flow control techniques have been a relevant research topic over the years. The usage of actuators to enhance the properties of NLF airfoils in terms of laminar flow is denoted as hybrid laminar flow control.

Most of the common active laminar flow control techniques are based on increasing the momentum of the near wall region of the boundary layer which leads to improved stability properties. It is well known that suction is a common method to keep a boundary layer laminar and the most common actuators in flow control are fluidic actuators (Cattafesta and Sheplak, 2011). The plasma actuator (PA) as a flow-control device is relatively new and the lack of moving parts, its short response time and the simple construction principle makes it suitable for active flow control. The application of the plasma actuators for different flow-control approaches has been reviewed by Moreau (2007) and Corke et al. (2010). The fluid dynamic efficiency of the PA is only in the order of 0.1% and this requires a smart application of the actuator in order to reach a total energy saving as discussed by Kriegseis et al. (2013a).

A recent approach for laminar flow control is the active cancelation of disturbances in the boundary layer by superposition before they lead to an early transition to turbulence. Downstream propagating waves are sensed by a surface mounted sensor and directly canceled by an appropriate actuator. This approach, called active wave cancelation (AWC), has been investigated with different actuator types such as moving wall actuators (Sturzebecher, Nitsche, 2003, Thomas, 1983). The first experiments on the cancelation of artificially induced harmonic Tollmien–Schlichting (TS) waves with the DBD plasma actuator were conducted by Grundmann and Tropea (2008). The control algorithms for this kind of flow control have been developed further over the years. While the numerical investigations mainly focussed on model based control techniques (Fabbiane et al., 2014), the experimental community mostly used adaptive control algorithms such as the fxLMS (filtered-x Least-Mean-Squares) algorithm. The use of adaptive algorithms for wind-tunnel and in-flight (Kurz et al., 2014) experiments is based on the robustness of the control algorithms and their ability to adapt to slight changes of the flow parameters, which result in changes of the growth rates and propagation speed of the disturbances in the boundary layer.

Active flow control in future technical applications will have to cope with changing flow conditions and should work reliably over a certain range of operation conditions. The presented work investigates and evaluates the robustness and stability of a fxLMS controller under varying free-stream velocities in a flat-plate wind-tunnel experiment. The investigations described in the following do not only affect active-wave cancelation with plasma actuators but also the application of the fxLMS algorithm for laminar-flow control in general. The experimental setup with sensors, disturbance source, actuator and the control algorithm is described in Section 2. The base-flow case and the dynamic transmission behavior of the boundary layer are systematically investigated in Section 3. The stability of the basic fxLMS controller with a constant secondary path model H^ec and its robustness against changes of the free-stream velocity is investigated in Section 4, focusing on changes of the disturbances’ phase speed and its connection to the controller stability. Finally, Section 5 presents a method for extending the range of operation of a fxLMS controller by continuously adapting the secondary path model H^ec during operation. Concluding remarks summarize the the major results in Section 6.

Section snippets

Experimental setup

The experiments are conducted in an open-circuit Eiffel type wind tunnel at TU Darmstadt, which provides an 450 mm × 450 mm test section and an averaged turbulence intensity of Tu=0.1%, measured at the end of the 1:24 contraction nozzle. A 1600 mm long flat plate, equipped with an 1:6 elliptical leading edge and an adjustable trailing edge, is mounted horizontally at half height of the test section. The wind-tunnel velocity UWT is varied from 7 m/s to 17 m/s whereas a wind-tunnel speed of UWT=12

Base flow characterization

Hot-wire boundary-layer measurements have been carried out to characterize the flow for the reference case at a wind-tunnel speed of UWT=12m/s, which corresponds to a free-stream velocity of the flat-plate boundary layer of U=14m/s due to blockage. The linear stability theory (LST) calculations for the reference case UWT=12m/s are shown in Fig. 5, assuming a 2D wave front (spanwise wave number β=0) and a Blasius boundary layer. All stability calculations in this manuscript have been performed

Stability of the fxLMS controller

Successful TS-wave cancelation experiments with broad-band disturbances have been documented in the literature before (e.g. Fabbiane, Simon, Fischer, Grundmann, Bagheri, Henningson, 2015, Sturzebecher, Nitsche, 2003). This section discusses the stability of the control algorithm for changes in UWT based on the investigation on the boundary-layer transmission behavior in Section 3.2. An example for wave attenuation at UWT=13m/s is shown in Fig. 16. The TS-wave “hump”, which ranges from about 120

Adaptive secondary path

The fxLMS controller has shown a robust behavior in a certain operation range, corresponding to ± 90° phase-angle error (Section 4). In order to extend the operational range of the controller it is necessary to adapt the secondary path online (Elliott, 2000, Kuo, Morgan, 1995). Several methods for the continuous online identification of secondary paths have been investigated within the last decades (e.g. Zhang et al., 2003). However, these methods are usually very application specific and

Conclusions

The stability of an adaptive fxLMS control algorithm for canceling broad-band Tollmien–Schlichting waves with a DBD plasma actuator has been investigated for changing free-stream velocities in a flat plate boundary layer. The main focus of the work was put on the phase-angle error depended stability of the controller and its flow-physical background, explained by linear stability theory. The basic fxLMS controller is able to adapt changes in the physical secondary path Hec of ± 90° compared to

Acknowledgments

This work was supported by the German research foundation (DFG) under the grant No. GR 3524/4-1.

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